Simple enough, will just take an amazingly long time to execute. Defeat the amount of enemies listed. Defeated enemies MUST have been killed by Edge (Killing blow landed, does not matter if computer helps, as long as Edge gets the final shot)

009: Land 1,000 hits in total
030: Land 3,000 hits in total
049: Land 10,000 hits in total
070: Land 30,000 hits in total
090: Land a total of 99,999 hits
051: Press 10,000 buttons
091: Press 100,000 buttons

Landing a hit is determined when your sword actually strikes the target and deals damage. Button presses are any time you hit a button on your controller, (Assuming it only counts the 'A' button,) so you can rapid fire those 2 BT's, (meaning if you click 'A' five times during Edge's attack you'll get 1 hit awarded, but 5 button presses awarded.)

A blindside is activated when you hold B and move the analog stick in a direction to slip behind an enemy. Blindsides are only counted when you are in 'Short' range to your target, so long range jumps do not count.

The bugs in Aeos are perfect targets to get Blindsides, as they are very quick to recover if you do not attack them, letting you Blindside around once every 5 seconds.

In order to unlock these you will need max ATK and a monster with a lot of health, combo together a bunch of Reaper Strikes and equip extra crits. Buff yourself with 3 stacks of Enhance and use a max level Berserking. From there keep using it again and again, eventually you'll hit a crit for enough damage.

For without a weapon, you can equip items like the Spriggan Monster Jewel, which doubles your ATK, to help negate the ATK lost from not having a weapon on.

For 5555 damage, Give Edge 2745 attack and fight Gerel's on planet Aeos, blindside them and attack, you should be hitting for close to this damage range. Keep going until you get the BT. Adjust your attack as needed if damage is too far off.

For 55,555 damage, give Edge 7182 attack and use Raging Strike on Crater Perytons in the Seven Star ruins on the first floor.

The ability to lengthen your Rush Mode time is acquired by leveling up BEAT: B at higher levels you gain the ability for a slower Rush Mode Decay and at max level the ability to increase your rush gauge during Rush Mode.

Level your BEAT:B with rush to 20, then enter a battle with something from Nox Obscurus (preferrably a melee unit), take off your weapon and spam a fast hitting move again and again. You'll get them both eventually, usually with a bit of luck that the enemy dosen't guard everything.

Simple enough, defeat the amount of enemies listed. Defeated enemies MUST have been killed by Edge (Killing blow landed, does not matter if computer helps, as long as Edge gets the final shot)

Humanoids are the only creatures that count for this, you can tell if it is a humanoid if it stands on 2 legs and has 2 hands. Fighting Sydonaist's inside the purgatorium is your best bet, as you can easily one shot them.